You are high in the morning because the Lantus you injected the previous morning has run out of steam during the night. Try splitting the dose into 10 units before bed and 10 units when you get up and see what difference it makes. It should spread the Lantus action more eveny over the day. The conversion is easy. Simply halve your morning dose and take the other half before going to bed that night.
When you have done that, test your basal doses using the method described
here. Then you can tweak the dosages and/or use different insulins until you get the desired effect.
